Do a state function be multu-valued function

A thermodynamic state function should be single valued function of independent varibles.
In case of steamtables of pure water, there is same entahlpy (U=2000 kJ/kg) at temperature T1=700K and pressure P1=63.458 MPa, and at T2=700K and P2=456.356 MPa. Thus U is a multiple valued function for pure water. How it can be explained with the basic laws of thermodynamics.

If we consider T and H as independent variables, it is impossible to predict the right value of P. The meaning of two values of P is that P is not an exact solution. This way- thermodynamics is not an Exact Science. Everyone knows that thermodynamic is an exact science, therefore the two values of P in the above situation are incorrect.

Let us further exemplify the above situation. We have a container filled with water at T=700 K and P=63.485 MPa. Since there is same H (2000 kJ/kg) for P= 63.458 MPa and 456.356 MPa at T= 700 K, it means we can pressurize (from 63.458 to 465.356 MPa) the container without any work. In other words, we can increase the pressure in a system of constant V and T without doing any work. If it is possible, we can develop a Carnot cycle to solve the world energy problem with no expense.

If a state function has multiple values, either the definition is incorrect or the data.

State variables have to be single valued. The Gibbs-Duhem relation relies on this. If they weren't single valued, then a closed path on a state diagram could result in a change of the state variable.. that is the value of the variable would be path-dependent, which is the definition of something that is not a state variable, but a process variable.

Yes, you are right. A state function has to be single valued function. It is a definition or based on the some relation. It is not the question, the question is that the steam Tables for pure water which is published in a NIST and AIP journal, J. Phys. Chem. Ref. Data, 2000, has multiple values for U, H and G.

It is really amazing the institutes producing standards for whole scientific community, do not know (or do not accept) that a state function should be single valued function.

I wrote an article on it to demonstrate the problem with the steam tables. Similarly, I proposed a method to measure the properties of water (liquid) correctly. I have big discussion the editor of JPCRD and the authority.

Their reply is that a state function can have multiple values. So, the steam tables of water has no problem.

If anyone is interested in reading it. I can send a copy. Just send me your email. my email is mahendra@iie.org.mx

If the thermodynamic properties of water are incorrect, there is problem in understading the natural processes on the earth.